Dynamical systems generated by various types of pin mixers were studied for the application to the single-screw extruders. A periodic unit of the pin mixer was modeled as a dynamical system of the complex duct flow. It was found that the cross-sectional space could be divided into two distinct regions: the inner and outer zones. The pin configuration directly affects the motion of fluid particles in the inner region, while motion in the outer region is governed by the resonance phenomena. The effects of the number of pins, the pin height, the pin orientation, and the composition of two different pin units were studied with the numerical results and explained in the language of the dynamical systems theories. Finally, the validity of our modeling, and the numerical result was verified by qualitative comparison with experimental results. (C) 2004 American Institute of Chemical Engineers.